Properties

Label 1568.2.i
Level $1568$
Weight $2$
Character orbit 1568.i
Rep. character $\chi_{1568}(961,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $25$
Sturm bound $448$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1568.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 25 \)
Sturm bound: \(448\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1568, [\chi])\).

Total New Old
Modular forms 512 80 432
Cusp forms 384 80 304
Eisenstein series 128 0 128

Trace form

\( 80q - 40q^{9} + O(q^{10}) \) \( 80q - 40q^{9} + 16q^{13} - 32q^{25} - 16q^{29} + 8q^{33} - 8q^{37} - 16q^{41} + 8q^{45} + 8q^{53} + 80q^{57} + 24q^{61} - 24q^{65} - 24q^{73} - 96q^{81} + 112q^{85} - 40q^{89} - 24q^{93} + 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1568, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1568.2.i.a \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-2\) \(0\) \(q+(-2+2\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1568.2.i.b \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
1568.2.i.c \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
1568.2.i.d \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(0\) \(q+(-2+2\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1568.2.i.e \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) \(q-4\zeta_{6}q^{5}+3\zeta_{6}q^{9}-4q^{13}+(-8+\cdots)q^{17}+\cdots\)
1568.2.i.f \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}-6q^{13}+(2-2\zeta_{6})q^{17}+\cdots\)
1568.2.i.g \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+6q^{13}+(-2+\cdots)q^{17}+\cdots\)
1568.2.i.h \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) \(q+4\zeta_{6}q^{5}+3\zeta_{6}q^{9}+4q^{13}+(8-8\zeta_{6})q^{17}+\cdots\)
1568.2.i.i \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+(2-2\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
1568.2.i.j \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
1568.2.i.k \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
1568.2.i.l \(2\) \(12.521\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(2\) \(0\) \(q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
1568.2.i.m \(4\) \(12.521\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(-2\) \(-2\) \(0\) \(q+(-1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
1568.2.i.n \(4\) \(12.521\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(-2\) \(2\) \(0\) \(q+(-1-\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1568.2.i.o \(4\) \(12.521\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(2\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(2\beta _{1}-\beta _{2}+2\beta _{3})q^{5}+\cdots\)
1568.2.i.p \(4\) \(12.521\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{1}q^{3}+3\beta _{2}q^{5}+4\beta _{2}q^{9}+\beta _{1}q^{11}+\cdots\)
1568.2.i.q \(4\) \(12.521\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{9}+(-2-2\beta _{2})q^{11}+\cdots\)
1568.2.i.r \(4\) \(12.521\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{9}+(2+2\beta _{2})q^{11}-2\beta _{3}q^{13}+\cdots\)
1568.2.i.s \(4\) \(12.521\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+3\beta _{1}q^{5}+(3+3\beta _{2})q^{9}+5\beta _{3}q^{13}+\cdots\)
1568.2.i.t \(4\) \(12.521\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}+(3+3\beta _{2})q^{9}+\beta _{3}q^{13}+(-5\beta _{1}+\cdots)q^{17}+\cdots\)
1568.2.i.u \(4\) \(12.521\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{2}q^{3}+(1-\zeta_{12})q^{5}+3\zeta_{12}^{2}q^{11}+\cdots\)
1568.2.i.v \(4\) \(12.521\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(2\) \(-2\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
1568.2.i.w \(4\) \(12.521\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(2\) \(2\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
1568.2.i.x \(4\) \(12.521\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(2\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+(-2\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+\cdots\)
1568.2.i.y \(8\) \(12.521\) 8.0.207360000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+(-2\beta _{1}+2\beta _{4})q^{5}-7\beta _{3}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1568, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1568, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)